Geometric shapes have been in music since it was first notated, and perhaps even before, in the guise of tone painting. For example; waves, the sign of the cross, high/low, etc. are all pictures that can be drawn in music. Interest in mathematical approaches to music has been around for some time.
The Schillinger Method of Music Composition of the early/middle 20th century takes this point of view in a traditional tonal melody and harmony context. After WWII, with its focus on pre-compositional, and/or non-tonal material, it became possible for more literal projection of geometry in music. For example, to hold a single note, or cluster, for 3 hours would project a straight line. European interest in compositional possibilities of timbre and density over melody and harmony create a perfect platform to use geometry, or shapes to create formal design.
Consider your compositional space by registers (top high, bottom low) as a large blank rectangular page, pick a shape within; say a side view of a Volkswagen bug. Consider that timbre and density can be thematic objects. Timbre; by making all other musical aspects indistinct except for timbre. For example, an orchestra’s violin section can be divided into single parts, each playing its lowest 4 notes in a slightly different heterophonic rhythmic formation so only the timbre stands out. Density; by increasing the register coverage or altering the speed of the above formations (faster more dense), or by thinning , fewer notes say 3 or 2, or by thickening that is adding more notes, or by switching from chromatic to diatonic formations. Articulation and bowings can also create contrasting timbre.
Lesson 14 Practice:
Now using timbre densities and register draw a triangle three different ways; create the walls (connect the dotes) fill in the triangle itself, then combine the two. Try music painting a car your “bug” —it probable will be most dense in the center then gradually fade away (though the wheels will project into the lower registers).